On weak sequential convergence in JB*-triple duals

• Autorzy: Leslie J. Bunce , Antonio M. Peralta
• Języki publikacji: EN

Abstrakty

EN

We study various Banach space properties of the dual space E* of a homogeneous Banach space (alias, a JB*-triple) E. For example, if all primitive M-ideals of E are maximal, we show that E* has the Alternative Dunford-Pettis property (respectively, the Kadec-Klee property) if and only if all biholomorphic automorphisms of the open unit ball of E are sequentially weakly continuous (respectively, weakly continuous). Those E for which E* has the weak* Kadec-Klee property are characterised by a compactness condition on E. Whenever it exists, the predual of E is shown to have the Kadec-Klee property if and only if E is atomic with no infinite spin part.

Kategorie tematyczne

• 46L70: Nonassociative selfadjoint operator algebras
• 46L05: General theory of C * -algebras
• 17C65: Jordan structures on Banach spaces and algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 160
• Numer: 2
• Strony: 117-127

Daty

wydano

2004

Twórcy

autor

Leslie J. Bunce

• University of Reading, Reading RG6 2AX, Great Britain

autor

Antonio M. Peralta

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm160-2-2